# ckks tutorial

Published articles for ckks tutorial.

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## CKKS -- Polynomials, the Canonical Embedding, and Encoding

DevFeed: [CKKS -- Polynomials, the Canonical Embedding, and Encoding](<https://devfeed.tech/articles/ckks-polynomials-the-canonical-embedding-and-encoding-40495.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2026/04/29/ckks-polynomials-the-canonical-embedding-and-encoding/>)

Published: 2026-04-29T12:25:44Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [homomorphic encryption](<https://devfeed.tech/topics/homomorphic-encryption.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>)

Tags: [ckks](<https://devfeed.tech/tags/ckks.md>), [ckks-tutorial](<https://devfeed.tech/tags/ckks-tutorial.md>), [cryptography](<https://devfeed.tech/tags/cryptography.md>), [encoding](<https://devfeed.tech/tags/encoding.md>), [encryption](<https://devfeed.tech/tags/encryption.md>), [homomorphic-encryption](<https://devfeed.tech/tags/homomorphic-encryption.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [neural-network](<https://devfeed.tech/tags/neural-network.md>), [polynomial-ring](<https://devfeed.tech/tags/polynomial-ring.md>), [polynomials](<https://devfeed.tech/tags/polynomials.md>), [programming](<https://devfeed.tech/tags/programming.md>), [python](<https://devfeed.tech/tags/python.md>), [technical](<https://devfeed.tech/tags/technical.md>), [tutorial](<https://devfeed.tech/tags/tutorial.md>)

### AI overview

This tutorial introduces the CKKS homomorphic encryption scheme and develops mathematical background on the polynomial ring used in its basic formulation and the canonical embedding used to encode cleartext messages as plaintexts. It also outlines CKKS's history, including its support for approximate arithmetic and later bootstrapping improvements.

### Source excerpt

Table of Contents In this tutorial series, I will introduce the CKKS homomorphic encryption scheme from the ground up, in rather intricate detail. Each article in this series corresponds to a pull request on a GitHub repository. The code for this article is in this pull request. Follow along by cloning the repository and checking out the code at the relevant commit. This first article will cover some of the mathematical background necessary in the formulation of the CKKS encryption scheme, specifically the polynomial ring used in the most basic version of CKKS, and the canonical embedding used to encode cleartext messages as plaintexts.